Question

0.142857,Given real number is expressed in decimal form. Find whether they are rational or not. If rational, express them in the form p/q. Comment on factors of q.

Answer 1

Question : 0.142857142857……

ANSWER : 0.142857142857…… is non terminating recurring, so it is a rational number.

SOLUTION IS IN THE ATTACHMENT...

REAL NUMBERS :

a number which is either rational or irrational is called a real number.

RATIONAL NUMBERS :

A number that can be expressed as p/q , where p,q are Integers and q≠0 is called a rational number.

IRRATIONAL NUMBERS :

A number that cannot be expressed as p/q , where p,q are Integers and q≠0 is called a irrational number.

NON TERMINATING REPEATING DECIMAL EXPANSION :

The number which does not terminate but repeat the particular number again and again in the process of division , is said to be a non terminating repeating decimal expansion.

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

Hi,

0.142857 is a rational number .

Since it is a terminating decimal.

0.142857

= 142857/1000000

= 142857/( 10^6 )

= 142857/( 2^6 × 5^6 )

= p/q

denominator q is the form 2^n × 5^m,

( n = 6 and m = 6 )

I hope this helps you.

: )